Calculating Ixy ?


by phydis
Tags: None
phydis
phydis is offline
#1
Jul22-13, 03:22 AM
P: 28
Here as shown in the diagram,

(1)Is Ixy zero for plane ABCD symmetrical along X axis? If yes, how it happens?
(2)How can we calculate Ixy for the plane PQRS ?

Ixy = the product of moment of area.

Thanks!
Attached Thumbnails
Ixy.jpg  
Phys.Org News Partner Physics news on Phys.org
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Mapping the road to quantum gravity
Chameleon crystals could enable active camouflage (w/ video)
SteamKing
SteamKing is offline
#2
Jul22-13, 06:58 AM
HW Helper
Thanks
P: 5,599
For any plane figure with an axis of symmetry, Ixy = 0 for coordinate axes thru the centroid of the figure.

To confirm this, examine the definition of Ixy = Int(x*y)dA For every element of area dA which lies on one side of the axis of symmetry, there will be a corresponding element of area lying on the opposite side which is the same distance from the axis. When you add up all of these elements of area multiplied by x*y, the integral is necessarily equal to zero.

To calculate the Ixy of rectangle PQRS, apply the parallel axis theorem.


Register to reply

Related Discussions
Calculating e3? Engineering, Comp Sci, & Technology Homework 1
Calculating n given r and nCr? Set Theory, Logic, Probability, Statistics 4
Calculating angles,calculating velocity General Engineering 2
Calculating Pi Computing & Technology 4
Calculating dd.mm.ss Calculus 1